Finite Group DatabasebetaFinite Group Databasebeta| order | 29718 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#23755290 |
| Fitting, socle, derived | C3×C13×C127 ⋊ C2×C3 |
| Hall | C3×#19097153 ⋊ C2 |
| Hall | C13×C127 ⋊ C3×D3 |
| Sylow | C127 ⋊ C3⋊(D13⋊C3) |
| Sylow | C13 ⋊ C3⋊(D127⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C127 | C2×C3 |
| LCS | G ▷ C3×C13×C127 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 4953 |
A minimal faithful permutation representation — 2 generators on 143 points:
(2,3)(5,9,10,6,7,11)(8,15,14,12,13,16)(18,22,23,19,20,24)(21,30,31,25,26,40)(27,43,44,33,34,57)(28,42,38,36,32,29)(35,62,63,46,47,80)(37,60,61,49,45,54)(39,41,59,51,52,55)(48,85,86,65,66,109)(50,83,84,68,64,77)(53,58,82,70,71,78)(56,98,96,74,75,73)(67,114,90,88,89,116)(69,112,113,91,87,106)(72,81,111,93,94,107)(76,124,125,99,100,102)(79,129,122,103,104,97)(92,137,121,118,115,135)(95,110,117,119,120,136)(101,141,140,126,127,133)(105,143,142,130,131,128)(108,138,139,132,134,123);(1,2,3)(4,5,8,7,11,14,13,15,16,10,9,12,6)(17,18,21,27,35,48,67,90,117,138,143,141,137,114,118,91,68,49,36,20,24,29,39,53,72,95,121,86,111,129,124,112,85,110,126,99,74,52,26,32,40,54,73,97,123,140,113,63,82,98,83,62,81,108,130,103,71,34,45,55,57,77,102,128,142,125,84,44,59,60,43,58,79,105,132,94,47,64,75,78,80,106,133,139,122,96,61,31,42,30,41,56,76,101,120,66,87,100,104,107,109,135,119,93,70,51,38,23,22,28,37,50,69,92,89,115,127,131,134,136,116,88,65,46,33,25,19)Polycyclic presentation:
2,3^2,13,127|c^a=c^2,d^a=d^12,e^a=e^126,d^b=d^3,e^b=e^19834 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29718, 58);